# Page:Popular Science Monthly Volume 76.djvu/246

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THE POPULAR SCIENCE MONTHLY

required to drive the feed water pump), and the quantity of heat ${\displaystyle H_{2}}$ is delivered to the condenser.

According to the first law of thermodynamics, the work ${\displaystyle W}$ must be equal to ${\displaystyle H_{1}-H_{2}}$, both quantities of heat being expressed in energy units. Therefore

 ${\displaystyle W=H_{1}-H_{2}}$ (9)

As far as the net result is concerned the operation of the steam engine may be thought of as (a) the conversion into work of the whole of the heat H1 from temperature T1, and (b) the reconversion of a

Fig. 1.

portion ${\displaystyle H_{2}}$ of this work into heat at temperature ${\displaystyle T_{2}}$. The regeneration[1] associated with process (a) is equal to ${\displaystyle H_{1}/T_{1}}$ according to equation (8), and the degeneration associated with process (b) is equal to ${\displaystyle H_{2}/T_{2}}$ according to equation (8). If the operation of the engine involves sweeping processes, then the degeneration ${\displaystyle H_{2}/T_{2}}$ must exceed the regeneration ${\displaystyle H_{1}/T_{1}}$, that is, we must have

 style="text-align:center;"|${\displaystyle H_{2}/T_{2}>H_{1}/T_{1}}$ (10)

or, substituting the value of ${\displaystyle H_{2}}$ from equation (9) and solving for ${\displaystyle W}$, we have

 ${\displaystyle W<{\frac {T_{1}-T_{2}}{T_{1}}}H_{1}}$ (11)

The fractional part ${\displaystyle [(T_{1}-T_{2})/T_{1}]}$ of the heat ${\displaystyle H_{1}}$ which is converted into work by the engine is called the efficiency of the engine, and the inequality (11) shows that the efficiency of any engine working between temperatures ${\displaystyle T_{1}}$ and ${\displaystyle T_{2}}$ must be less than ${\displaystyle [(T_{1}-T_{2})/T_{1}]}$ whatever the nature of the working fluid and whatever the design of the engine.

The Perfect Engine.—An engine involving no irreversible or sweep-

1. To convert an amount of work ${\displaystyle W}$ into heat at a given temperature involves an amount of degeneration, and to convert the heat into work involves the same amount of what may be called thermodynamic regeneration.